Finite Group Databasebeta

← #119565

Subgroups — #119565

Order 512.

603 conjugacy classes of subgroups.

The subgroup lattice has 465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21885C211yesmaximal, characteristic
2#21337C211yesmaximal, characteristic
3#17486C211yesmaximal, characteristic
4#10848C211yesmaximal, characteristic
5#8095C211yesmaximal, characteristic
6C2×#1292C211yesmaximal, characteristic
7C2×#1283C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#423C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13C2×C4×M16C2211yescharacteristic
14#2285C2211yescharacteristic
15#1998—22no—
16#1997—21no—
17#1997—21no—
18#1987—21no—
19#1981—21no—
20#1892C414yes—
21#1803—22no—
22C2×#344—21no—
23C2×#344—21no—
24#1742—21no—
25#1742—21no—
26#1493—22no—
27#1487—22no—
28#1481—22no—
29#1303—22no—
30#1292—22no—
31#1283—22no—
32C22×M16—21no—
33C22×M16—21no—
34C22×M16D411yescharacteristic
35C22×M16D411yescharacteristic
36C23×C8C2×C412yes—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42#533—21no—
43#533—21no—
44#533—21no—
45C2×C4⋊Q8D411yescharacteristic
46C2×C4⋊Q8D411yescharacteristic
47C2×#125—21no—
48C2×C22⋊Q8—21no—
49C2×C22⋊Q8C2×C412yes—
50C2×C4×Q8—21no—
51C2×C4×Q8D412yes—
52C2×#117—21no—
53C2×#117—21no—
54C22×C42C2311yescharacteristic
55#431—21no—
56#431—21no—
57#431—21no—
58#431D412yes—
59#423—21no—
60#423—21no—
61#423—21no—
62#423—21no—
63#423—21no—
64#423—21no—
65#423D412yes—
66#423D412yes—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76C2×C4⋊C8—21no—
77C2×C4⋊C8—21no—
78C2×#103—24no—
79C2×C22⋊C8—21no—
80C4×M16—21no—
81C4×M16—21no—
82C4×M16—21no—
83C4×M16—21no—
84C2×#97—21no—
85C2×C4×C8—21no—
86C2×C4×C8—21no—
87#384—21no—
88#382—21no—
89#380—21no—
90#380C2×C412yes—
91C4×C4⋊C4—21no—
92C4×C4⋊C4—21no—
93#344—42no—
94#344—42no—
95#343—22no—
96#343—22no—
97#343—22no—
98#343—22no—
99#340—24no—
100Q8⋊C8—28no—
101C22×Q8—21no—
102C22×Q8C22⋊C412yes—
103C23×C4C22×C411yescharacteristic
104C23×C4C2×D411yescharacteristic
105C23×C4#4111yescharacteristic
106C2×M16—21no—
107C2×M16—21no—
108C2×M16—21no—
109C2×M16—21no—
110C2×M16—21no—
111C2×M16—21no—
112C2×M16—21no—
113C2×M16—21no—
114C2×M16—21no—
115C2×M16—21no—
116C2×M16—22no—
117C2×M16—22no—
118C2×M16—41no—
119C2×M16—41no—
120C2×M16—41no—
121C2×M16—41no—
122C2×M16—41no—
123C2×M16—41no—
124C2×M16—41no—
125C2×M16—41no—
126C2×M16—41no—
127C2×M16—41no—
128C2×M16SD1612yes—
129C2×M16Q1612yes—
130C22×C8—21no—
131C22×C8—21no—
132C22×C8—22no—
133C22×C8—22no—
134C22×C8—22no—
135C22×C8—41no—
136C22×C8—41no—
137C22×C8—41no—
138C22×C8—82no—
139C4⋊Q8—21no—
140C4⋊Q8—21no—
141C4⋊Q8—21no—
142C4⋊Q8—21no—
143C4⋊Q8—21no—
144C4⋊Q8—21no—
145C4⋊Q8—21no—
146C4⋊Q8—21no—
147#125—41no—
148#125—41no—
149#125—41no—
150#125—41no—
151C22⋊Q8—22no—
152C22⋊Q8—22no—
153C22⋊Q8—22no—
154C22⋊Q8—22no—
155C22⋊Q8—41no—
156C22⋊Q8—41no—
157C22⋊Q8—41no—
158C22⋊Q8—41no—
159C4×Q8—22no—
160C4×Q8—22no—
161C4×Q8—22no—
162C4×Q8—22no—
163C4×Q8—41no—
164C4×Q8—41no—
165C4×Q8—41no—
166C4×Q8—41no—
167#117—41no—
168#117—41no—
169#117—41no—
170#117—41no—
171#117—41no—
172#117—41no—
173#117—41no—
174#117—41no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4C22⋊C412yes—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C42—22no—
187C2×C42—41no—
188C2×C42C2×D411yescharacteristic
189C2×C42C2×D411yescharacteristic
190C2×C42C2×D411yescharacteristic
191C2×C42C2×D411yescharacteristic
192C2×C42C2×D411yescharacteristic
193C2×C42#4111yescharacteristic
194C2×C42#4111yescharacteristic
195C2×C42#4111yescharacteristic
196C2×C42#4111yescharacteristic
197C2×C42#4111yescharacteristic
198C2×C42#4111yescharacteristic
199C2×C42#4111yescharacteristic
200C4⋊C8—22no—
201C4⋊C8—22no—
202C4⋊C8—22no—
203C4⋊C8—22no—
204C4⋊C8—22no—
205C4⋊C8—41no—
206C4⋊C8—41no—
207C4⋊C8—41no—
208C4⋊C8—41no—
209C4⋊C8—41no—
210C4⋊C8—41no—
211C4⋊C8—41no—
212C4⋊C8—41no—
213C4⋊C8—41no—
214#103—84no—
215C22⋊C8—22no—
216C22⋊C8—41no—
217#97—41no—
218#97—41no—
219C4×C8—22no—
220C4×C8—41no—
221C4×C8—41no—
222C4×C8—41no—
223#95—22no—
224#95—41no—
225C24C4×D411yescharacteristic
226C2×Q8—22no—
227C2×Q8—22no—
228C2×Q8—42no—
229C2×Q8—42no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—82no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—42no—
238C22×C4—81no—
239C22×C4C2×C22⋊C411yescharacteristic
240C22×C4#11711yescharacteristic
241C22×C4#11711yescharacteristic
242C22×C4C4×D411yescharacteristic
243C22×C4C4×D411yescharacteristic
244C22×C4C4×D411yescharacteristic
245C22×C4#12011yescharacteristic
246C22×C4#12111yescharacteristic
247C22×C4#12111yescharacteristic
248C22×C4#12111yescharacteristic
249C22×C4#12111yescharacteristic
250C22×C4#12311yescharacteristic
251C22×C4#12311yescharacteristic
252C22×C4#12311yescharacteristic
253C22×C4#12411yescharacteristic
254C22×C4#12411yescharacteristic
255C22×C4#12611yescharacteristic
256C22×C4#12611yescharacteristic
257C22×C4C2×SD1611yescharacteristic
258C22×C4C2×Q1611yescharacteristic
259C22×C4#13511yescharacteristic
260C22×C4#13511yescharacteristic
261C22×C4AGL(1,ℤ/8)11yescharacteristic
262C22×C4#13711yescharacteristic
263C22×C4#13711yescharacteristic
264C22×C4#13711yescharacteristic
265M16—22no—
266M16—22no—
267M16—22no—
268M16—22no—
269M16—41no—
270M16—41no—
271M16—41no—
272M16—41no—
273M16—42no—
274M16—42no—
275M16—42no—
276M16—42no—
277M16—81no—
278M16—81no—
279M16—81no—
280M16—81no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—44no—
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—42no—
291C2×C8—42no—
292C2×C8—82no—
293C2×C8—81no—
294C2×C8—81no—
295C2×C8—81no—
296C2×C8—81no—
297C2×C8—82no—
298C2×C8—82no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—42no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—42no—
310C4⋊C4—42no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—82no—
314C4⋊C4—81no—
315C4⋊C4—81no—
316C22⋊C4—42no—
317C22⋊C4—42no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C42—42no—
321C42—42no—
322C42—81no—
323C42—81no—
324C42#12011yescharacteristic
325C42#12111yescharacteristic
326C42#12111yescharacteristic
327C42#12111yescharacteristic
328C42#12111yescharacteristic
329C42#12311yescharacteristic
330C42#12311yescharacteristic
331C42#12311yescharacteristic
332C42#12311yescharacteristic
333C42#12311yescharacteristic
334C42#12311yescharacteristic
335C42#12311yescharacteristic
336C42#12411yescharacteristic
337C42#12411yescharacteristic
338C42#12611yescharacteristic
339C42#12611yescharacteristic
340C23—41no—
341C23—41no—
342C23#38611yescharacteristic
343C23#38811yescharacteristic
344C23#38811yescharacteristic
345C23C4×SD1611yescharacteristic
346C23C4×Q1611yescharacteristic
347C23#44011yescharacteristic
348C23#44111yescharacteristic
349Q8—44no—
350Q8—42no—
351Q8—42no—
352Q8—82no—
353Q8—82no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—82no—
372C2×C4—82no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4—82no—
376C2×C4#38111yescharacteristic
377C2×C4#38611yescharacteristic
378C2×C4#38811yescharacteristic
379C2×C4#38811yescharacteristic
380C2×C4#39411yescharacteristic
381C2×C4#39411yescharacteristic
382C2×C4#39411yescharacteristic
383C2×C4#39411yescharacteristic
384C2×C4#39711yescharacteristic
385C2×C4#39711yescharacteristic
386C2×C4#39711yescharacteristic
387C2×C4#39711yescharacteristic
388C2×C4#44811yescharacteristic
389C2×C4#44911yescharacteristic
390C2×C4#45111yescharacteristic
391C2×C4#45211yescharacteristic
392C2×C4#46011yescharacteristic
393C2×C4#46111yescharacteristic
394C2×C4#46211yescharacteristic
395C2×C4#46211yescharacteristic
396C2×C4#46311yescharacteristic
397C2×C4#46411yescharacteristic
398C2×C4#46411yescharacteristic
399C2×C4#46411yescharacteristic
400C2×C4#46511yescharacteristic
401C2×C4#46711yescharacteristic
402C2×C4#46811yescharacteristic
403C2×C4#47011yescharacteristic
404C2×C4#48311yescharacteristic
405C2×C4#48411yescharacteristic
406C2×C4#48511yescharacteristic
407C2×C4#48511yescharacteristic
408C2×C4#48711yescharacteristic
409C2×C4#48811yescharacteristic
410C2×C4#48911yescharacteristic
411C2×C4#49111yescharacteristic
412C8—42no—
413C8—42no—
414C8—82no—
415C8—82no—
416C8—82no—
417C8—82no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22#144011yescharacteristic
429C22#187811yescharacteristic
430C22#188011yescharacteristic
431C22#192711yescharacteristic
432C22#192811yescharacteristic
433C22#193311yescharacteristic
434C22#193511yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—82no—
443C4—82no—
444C4—162no—
445C4#191411yescharacteristic
446C4#191511yescharacteristic
447C4#203511yescharacteristic
448C4#203611yescharacteristic
449C4#204211yescharacteristic
450C4#204311yescharacteristic
451C4#205511yescharacteristic
452C4#205611yescharacteristic
453C4#207211yescharacteristic
454C4#207411yescharacteristic
455C2—21no—
456C2—21no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2#1117311yescharacteristic
462C2#1117911yescharacteristic
463C2#1119011yescharacteristic
subgroupG/H
center, socleC22#1440
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#218852
#213372
#174862
#108482
#80952
C2×#12922
C2×#12832